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Abstract Argumentation via Monadic Second Order Logic

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Scalable Uncertainty Management (SUM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7520))

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Abstract

We propose the formalism of Monadic Second Order Logic (MSO) as a unifying framework for representing and reasoning with various semantics of abstract argumentation. We express a wide range of semantics within the proposed framework, including the standard semantics due to Dung, semi-stable, stage, cf2, and resolution-based semantics. We provide building blocks which make it easy and straight-forward to express further semantics and reasoning tasks. Our results show that MSO can serve as a lingua franca for abstract argumentation that directly yields to complexity results. In particular, we obtain that for argumentation frameworks with certain structural properties the main computational problems with respect to MSO-expressible semantics can all be solved in linear time. Furthermore, we provide a novel characterization of resolution-based grounded semantics.

Dvořák’s and Woltran’s work has been funded by the Vienna Science and Technology Fund (WWTF) through project ICT08-028 and Szeider’s work has been funded by the European Research Council (ERC), grant reference 239962 (COMPLEX REASON).

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Author information

Authors and Affiliations

  1. Theory and Applications of Algorithms Group, University of Vienna, Austria

    Wolfgang Dvořák

  2. Institute of Information Systems, Vienna University of Technology, Austria

    Stefan Szeider & Stefan Woltran

Authors
  1. Wolfgang Dvořák
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  2. Stefan Szeider
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  3. Stefan Woltran
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  1. Department of Mathematics and Computer Science, Marburg University, Hans-Meerwein-Strasse 6, 35032, Marburg, Germany

    Eyke Hüllermeier , Thomas Fober  & Bernhard Seeger ,  & 

  2. Department of Computer Science, Auckland University, 38 Princes St., 1010, Auckland, New Zealand

    Sebastian Link

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Dvořák, W., Szeider, S., Woltran, S. (2012). Abstract Argumentation via Monadic Second Order Logic. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-33362-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33361-3

  • Online ISBN: 978-3-642-33362-0

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